Slice the chicken breasts lengthwise (butterfly them, then cut in half) to create 4 thinner cutlets. Trim off any excess fat. Season the chicken generously with salt and pepper, and sprinkle with garlic powder. Dredge the chicken in flour.
In a skillet over medium-high heat, melt 2 tablespoons of butter with the olive oil. Once the pan is hot, cook the chicken for about 4-5 minutes per side until golden brown. Transfer the chicken to a plate.
Remove the pan from heat and add chicken broth, lemon juice, lemon zest, the remaining 2 tablespoons of butter, and capers. Scrape up any browned bits from the bottom of the pan to incorporate the flavor.
Stir in the heavy cream and return the pan to the heat. When the sauce starts to bubble, add the chicken back into the pan. For a version without cream, increase the chicken broth to ¾ cup.
Cook for another 5 minutes, or until the chicken is fully cooked through and the sauce has reduced to your desired thickness. If the sauce thickens too much, add more broth as needed.
Garnish with freshly chopped parsley and/or parmesan cheese, if desired, and serve immediately.